Confidence interval for a proportion, Basic Statistics

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The quick method for a confidence interval for a proportion uses p ±1/√n as an approximation for a 95% confidence interval.  The margin of error in this case is slightly larger than necessary. Suppose that a simple random sample of 500 motorcycle registrations finds that 68 of the motorcycles are Yamahas. Give a 95% confidence interval for the proportion of motorcycles in the population that are Yamahas using the quick method of chapter 3 and then by the more precise method of chapter 21.

What does the confidence level of a confidence interval tell you?

Suppose that a population has mean, µ, and standard deviation, σ.  What does the central limit theorem tell us about the distribution of the sample mean?

Government regulations indicate that the total weight of cargo in a certain kind of airplane cannot exceed 310 kg. On a particular day a plane is loaded with 100 boxes of a particular item only. Historically, the weight distribution for the individual boxes of this variety has a mean of 3.2 kg and standard deviation 0.4 kg.

a. Interpret the meaning of the "a mean of 3.2 kg" in terms of repeated samplng.

b. what is the distribution of the sample mean weight for the boxes (give the name of the distribution and appropriate parameter values)?  

c.  What is the probability that the government regulation is met?


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